1) Prove that AU(Bnc)= (AUC)N(AUC) 2)Let M-{1,3,n}, find the power set of set M

Q: GRO 5. Consider the infinite set of positive integers {1, 2, 3,..}. Find a way to name definite…

A: Consider the infinite set of positive integers.

Q: 11 Plot the points (2, 0), (2,-3 (2, 4). (2, 1), and (2,-1) Describe the collection of all points of…

A: topic - coordinate geometry

Q: Enter the number of ways of coloring the vertices of a regular 4-gon with 5 distinct colors modulo…

A: We have to find a number of ways of coloring the vertices of a regular 4-gon and 5 different colors.

Q: Ametric space (x,d) is complete if and only ifx has the cantor intersection property

A:

Q: 8. In a university examination, which was indeed very tough, 50% at least failed in "Statistics",…

A: P(failed in Statistics) = 0.50P(failed in Topology) = 0.75P(failed in Functional Analysis) =…

Q: Let S = Span}( 3 2 3 . Show that dim(S)=2. 3

A: Basis: Let V be a subspace of ℝn. A basis of V is a set of vectors v1, v2, ..., vm in V such that:…

Q: 10. Show that the interval (0, 1) is covered by the open intervals In (1/n, 1- 1/n), n 2 3, but (0,…

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Q: If the interval [2,7] is partitioned into n= 8 subintervals of equal length, what is Ax? Ax = |…

A:

Q: 0 (HINT: First move terms around so that all terns are positive)

A: To prove:             ∑k = 0n(-1)k nk = 0

Q: 2] [ State the Sequential Criterion Theorem.

A:

Q: If the interval [4,9] is partitioned into n = 5 subintervals of equal length, what is Ax? Ax = (Type…

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Q: For all sets A , B and C A ∪ ( B ∩ C ) = ( A ∪ B ) ∩ ( A ∪ C )

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Q: 3) Consider the subsets [0, 1] and [3,4] of R, the set of all real numbers with the euclidean…

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Q: 10. State the Gödel Incompleteness Theorem. On which school of the foundations of mathematics did…

A: Godel Incompleteness Theorem states that the mathematical ideas should not have contradictions. This…

Q: Find integers x and y such that 3220x + 6006y = gcd(3220,6006).

A:

Q: Be M, N subsets of space W. Then span (MUN) = span (M) +span (N)- %3D

A:

Q: Give 3 different examples of norms on Z (set of integers)

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Q: Theorem 1.10. A set is infinite if and only if there is an injection from the set into a proper…

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Q: Theorem 1.14. The set of all finite subsets of a countable set is countable.

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Q: 2. How many bit strings(strings of 1 or 0) of length 8 are there such that it contains no more nan 3…

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Q: rcise: Prove that every finite set S of R" has no accumulation point.

A: Proof of the the given theorem is given as

Q: (4.2) Let X = {1,2, 3, 4} and 7 = {0, {1,2,3} , {2, 3},{1},X} be the topology defined on X. (a) Show…

A:

Q: True or False: Consider the subsets (0, 1) and (2, 3) of R, the set of all real numbers with the…

A: The given statement is  Consider the subsets (0, 1) and (2, 3) of R, the set of all realnumbers with…

Q: exercise 1.4. Consider Z/24Z. Determine the set {5 . 1, 5 - 2, ...,5 · 23} =? where z is the class…

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Q: Sketch a model atleast 2 axioms of Pappus's Geometry and identify those axioms

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Q: Prove that all integer solutions form an enumerable set without using Fermat Theorem

A: Given: Set of all integer solutions To prove: Set of all integer solutions form an enumerable set.

Q: union of a collectionm of connected sets that have a point in common is conne

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Q: a. Suppose that we have a class with 30 students. Prove that at least two students will have been…

A: a. Suppose that we have a class with 30 students.Prove that at least two students will have been…

Q: Consider the subsets [0, 1] and [3, 4] of R, the set of all real numbers with the euclidean…

A: Consider the subsets [0, 1] and [3, 4] of R, the set of all real numbers with theeuclidean topology.…

Q: What is the maximum number of people you can invite so that at most 3 guests are born same month?…

A: The Pigeonhole Principle: If n + 1 objects are placed into n boxes, then some box contains at least…

Q: on N and the floor topology on N are Exercise 3.42. Show that standard (order) topology the same.

A: Standard topology: Standard topology on ℝ is generated by the basis on usual open intervals B=a,…

Q: 5. It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Create a proof for the fc

A: Given,           1.        ~R⊃~Q2.        ~R

Q: Prove that a selection of 7 numbers from the set {1, 2, . . . , 11} contains numbers m and n such…

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Q: An organization wants to assemble a cluster of n computers using wires and hubs. Each must have…

A: Solution of the problem as follows

Q: Specify the sets by roster, (a) (Even counting numbers less than 14) (b) (Positive muitiples of 7)…

A: To simply the sets in roaster form

Q: 8. Prove that a matroid is uniform if and only if every circuit meets every cocircuit.

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Q: Theorem 1.12. The union of countably many countable sets is countable.

A: We have to prove that the union of countably many countable sets is countable.

Q: Let S = {(1,1), (1, 2), (2, 1), (3, 2), (3,3)}. Consider the polytope conv(S). Write this set as {r…

A: The given set is S=1,1,1,2,2,1,3,2,3,3. We know that the polytope:…

Q: Sketch the set of prints determined by given Condition 러니 12-util =3 -i

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Q: 2) Let R be the set of all real numbers with the euclidean topology. Show that R has an uncountable…

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Q: Let S = {0, 1}. List all the strings of length 4 over S that contain three or more 0’s.

A: It is given that S = {0,1}.It is known that if n be the positive integer and given a finite set A,…

Q: Theorem 1.11. The union of two countable sets is countable.

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Q: Prove that Yational numbers la b) with equality multiplication and addition defined as Set s of…

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Q: 4. Prove that the sets (–1,5) and [-1,1) U {2} U (3, ∞) have the same cardinality

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Q: If the interval [3,10] is partitioned into n = 8 subintervals of equal length, what is Ax? Ax =…

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Q: 2| and determine for the sets, Represent the sets in the comples plane F- whether they are open,…

A: Taking z=x+iy, z-2≤z forms the following region in the complex plane.

Q: Theorem 1.13. The set Q is countable.

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Q: Let S = {0, 1}.  List all the strings of length 4 over S that contain three or more 1's. (Enter…

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Q: Find a polyomial f(x) of degree 3 that has the following zeros. -8, 3, 0

A: Given :  To determine the polynomial fx of degree 3 that has the following zeros : -8, 3, 0